(see the final paragraph of [1]}) one sees that
\((\pi _{U}\otimes \pi _{V})\circ \hat{\Delta }(x)=\sum _{(T,W)} T\,\pi _W(x)\,T^*\ \Big (\cong \bigoplus _W \pi _W(x)\Big ), \qquad x \in \mathcal {U}(G),\) 
